hi,i am trying to solve a simlified two-phase model for the dilute droplets motion in the air. It's derived from the traditional Eulerian two-phase model in which alfa represents the volume fraction of liquid./ (1) /The continuum and momentum equations are as below(for steady problems): par(alfa*u)/par(x)+par(alfa*v)/par(y)=0, par(alfa*u)/par(x)+par(alfa*v*u)/par(y)=Cu*alfa, par(alfa*v)/par(x)+par(alfa*v*v)/par(y)=Cv*alfa. /(2)/ if above equations are written into no-conservative form,it can be seen that the continuum equation can be decoupled from the momentum equatons . So I solve the momentum equations to get u and v firstly,then deal with the continuum eqution to get alfa. /(3)/I try to discretize the equations with FVM,and use the high resolution schemes to deal with the convection terms.but I found that alfa is difficult to converge and there exists some oscillations even when I use the upwind scheme. I read some relative paper on this topic, and most of them use the FEM to discritize the equations and adopt the artificial viscosity or SUPG term to stablize the solution. /(4)/Because of the lack of experience to solve this kind of hyperbolic problem, so I don't know how to go ahead. I wonder if there are some methods to stablize the solution when I use the FVM to discritize the equations. I will be grateful for any suggestions! MAXIMUS

yes,pressure term does not appear in this equations because it is assumed that the pressure's effect on the droplets motion is neglected. you can look the paper below: http://www.newmerical.com/Scientific..._MULTISHOT.pdf. I find the eigenvalues of the Jcobian matrix of these equations are equal to each other: write the equation in the form: par(Q)/par(t)+par(F)/par(x)+par(G)/Par(y),and the Jacobian Matrix A=par(F)/par(Q),B=par(G)/par(Q). I find the three eigenvalues of A are lemda(1,2,3)=u, and lemda(1,2,3)=v for Matrix B. So maybe it's not a rigorous hyperbolic equations?